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  • In a lottery game, you need to select 4 numbers from a pool of 25 . How many different combinations of numbers are possible?  Option: 1 2

In a lottery game, you need to select 4 numbers from a pool of 25 . How many different combinations of numbers are possible?
 

Option: 1

29652


Option: 2

84896


Option: 3

10520


Option: 4

12650


Answers (1)

best_answer

To calculate the number of different combinations of 4 numbers that can be selected from a pool of 25 , you can use the concept of combinations. The formula for combinations is given by:

\mathrm{ C(n, r)=\frac{n !}{(r !(n-r) !)}}

where " n " is the total number of items in the pool, and " r " is the number of items to be selected.

In this case, n=25 (the total number of numbers in the pool) and r=4 (the number of numbers to be selected). Plugging these values into the formula, we get:

\begin{aligned} \mathrm{C}(25,4)&=\frac{25 !}{(4 !(25-4) !) }\\ & =\frac{25 !}{(4 ! 21 !)} \\ & =\frac{(25 \times 24 \times 23 \times 22)}{(4 \times 3 \times 2 \times 1)} \\ & =12,650 \end{aligned}

Therefore, there are 12,650 different combinations of 4 numbers that can be selected from a pool of 25 in the lottery game.

Posted by

Sanket Gandhi

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